Conceptual-stochastic modeling of seasonal runoff using autoregressive moving average models and different scales of aggregation

"The statistical and phenomenological aspects of the runoff process observed on different scales of aggregation are taken as a priori information for the conceptually based stochastic modeling of seasonal runoff. Runoff is considered as the sum of two groundwater components, with over-year and subannual response lag, and of a purely random component representing the direct runoff. This scheme is equivalent to a linear system, with two parallel linear reservoirs plus a zero lag linear channel. The system output is the runoff, and the input is the effective rainfall, considered proportional to the direct runoff. Assuming the effective rainfall as a non-Gaussian periodic independent process and considering nonseasonal groundwater parameters, this conceptualization leads to an autoregressive and moving average (2, 2) stochastic process with periodic independent residual. Stochastic model parameters are directly related to the linear system coefficients, and the effective rainfall structure can be determined from the estimated model residual. In order to obtain parameter estimates consistent with the conceptual constraints, two estimation stages, on an annual and a seasonal basis, and an iterative procedure are needed. The model was applied to a number of time series of monthly streamflows in the Apennine regions of Italy with promising results.